Origin: “Dates back to the days
of stagecoaches, whose drivers were often intensely competitive,
seeking to charge past one another, on narrow roads, at grave danger
to life and limb. If the vehicle’s wheels became entangled, both would
be wrecked; if they were lucky, the wheels would only touch and the
coaches could still go.”

TOUCH AND GO is used as both a noun and adjective (‘touch-and-go) and
means a precarious situation in which the outcome is doubtful or
extremely uncertain for a time – a close flirtation with danger or
disaster. “It was touch and go after his surgery, but he pulled
through.” “He was familiar with the touch and go of guerilla warfare.”
It also has a second meaning of ‘quick action or movement,’ “One must
learn to deal with the touch and go of city traffic.’

The first appearance of ‘touch and go’ in a literal sense was in the
16th century (see quote below) as a verbal phrase (used as noun or
adjective) meaning to touch for an instant and immediately go away or
pass on; to deal with momentarily or slightly. In the early 19th
century the phrase took on its two other figurative meaning – 1)
adjective: [1812] Involving or characterized by rapid, slight, or
superficial execution; sketchy; casual, careless; instantaneous;
expeditious. 2) noun: [1815] precarious situation.

The familiar sense of ‘precarious situation’ originated in the early
19th century with reference to coach driving or ship pilotage and
appears to have been a literal allusion to a vehicle barely escaping
collision. Coach drivers used the term ‘touch and go’ for a narrow
escape after the wheels of two coaches touched in a near accident –
the wheels would TOUCH, there would be a moment of extreme anxiety,
but neither vehicle was stopped, and each could GO on. For sailors a
ship was said to ‘touch and go’ when its keel scraped the bottom
without stopping the boat or loosing a significant amount of speed. A
second nautical use referred to the practice of approaching the shore
to let off cargo or men, but in an attempt to save time and avoid the
involved procedure of stopping – not stopping. It has been speculated
by some that the great risk and uncertainty involved in this maneuver
spawned the expression.

Quote: <1549 “As the text doeth ryse, I wyl
TOUCHE AND GO a lyttle in euery place, vntyl I come vnto to
much.”—‘First Sermon Preached Before King Edward VI’ by Latimer, page
26> [[literally, touch on and go away, deal with momentarily]]

<1655 “Howsoever we may taste of it to bring on Appetite, let it be
but a TOUCH AND GO.”—‘Healths Improvement’ by Moufet & Bennet (1746),
page 59> [[literally, touch on and go away, deal with momentarily]]

<1812 “There is an art of writing for the Theatre, technically called
TOUCH AND GO. . . indispensable when we consider the small quantum of
patience which . . . a London audience can be expected to
afford.”—‘Rejected Addresses, or the New Theatrum Poetarum’ by H. & J.
Smith, preface, page 11> [[figuratively, superficial execution]]

<1815 “'Twas TOUCH AND GO—but I got my seat.”—‘Letters on Epistles to
the Romans’ by R. Wardlaw in ‘Sketches of Life’ by Alexander (1856),
vi. page 166> [[figuratively, precarious situation]]

<1832 “Free to introduce anecdotes, quotations, and all such
TOUCH-AND-GO things as the formality of an essay would not admit of.”—
‘Memoirs, Journal, and Correspondence’ (1854) by Thomas Moore, VI.
page 247> [[figuratively, superficial execution]]

<1887 “She caught [the horse]..by the mane, and though it was TOUCH
AND GO she managed to retain her seat.”—‘Cleverly Won’ by H. Smart,
ii> [[figuratively, precarious situation]] (Facts on File Encyclopedia
of Word and Phrase Origins, Facts on File Dictionary of Clichés,
Picturesque Expressions by Urdang, Brewer’s Dictionary of Phrase and
Fable)

I'd never contest a claim by Ken Greenwald relating to etymology. The OED is about his 25th port of call. His claim for a pre-1550 origin woud seem to rule out the aeroplane explanation. (Of course, the usage may well have been broadened to include this practice, but that's hardly addressing the origin of the phrase, which OP expressly asks for.)
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Edwin AshworthDec 17 '14 at 22:15

That is fair. Assuming any of the other explanations are valid, my contribution would not be useful. I didn't intend to contest the Greenwald response or any of the other responses in the answer by JoseK. I added it because I didn't see any mention of the aeroplane anywhere else, in the interest of completeness.
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tphummelDec 18 '14 at 17:49

It's not an 'answer', though it would be fine as a 'comment'.
–
Edwin AshworthDec 18 '14 at 22:06